State and output feedback fuzzy variable structure controllers for multivariable nonlinear systems subject to input nonlinearities

Abstract

This paper presents three fuzzy adaptive controllers for a class of uncertain multivariable nonlinear systems with both sector nonlinearities and dead zones: two first controllers are state feedbacks and the last controller is an output feedback. The design of the first controller concerns systems with symmetric and positive definite control–gain matrix, while the second control design is extended to the case of nonsymmetric control–gain matrix thanks to an appropriate decomposition, namely the product of a symmetric positive definite matrix, a diagonal matrix with diagonal entries +1 or −1, and a unity upper triangular matrix. The third controller is an output feedback extension of the second controller. In this controller, a high-gain observer is incorporated to estimate the unmeasurable states. An appropriate adaptive fuzzy logic system is used to reasonably approximate the uncertain functions. A Lyapunov approach is adopted to derive the parameter adaptation laws and prove the stability of those control systems as well as the exponential convergence of their underlying tracking errors within an adjustable region. The effectiveness of the proposed fuzzy adaptive controllers is illustrated through simulation results.